Nonextensive Statistical Mechanics

4.4 Correlated Anomalous Diffusion 115withwhereandp q (x, t) = {1 − (1 − q)β(t)[x − x M(t)] 2 } 1/(1−q)Z q (t), (4.22)β(0)[β(t) = Zq (t)] 2=[(1 − 1 )e − t/τ + 1 ] 23−q, (4.23)Z q (0)K 2 K 2K 2 ≡k 2, (4.24)2(2 − q)D q β(0)[Z q (0)]q−1τ ≡1k 2 (3 − q) . (4.25)To close this discussion, let us mention that it can be straightforwardly shownthat∫dx p q (x, t) = 1, ∀t ≥ 0. (4.26)(x) Lévy distributions asymptotically satisfyL γ (x) ∝ 1|x| 1+γ (|x| →∞;0